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Math 9

Math 9 · Worksheets

Linear equations and inequalities

Ten questions of mixed difficulty, covering Equations and inequalities. Print it, or work through it on screen — the answer key starts on its own page.

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Linear equations and inequalities

Math 9 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. Gym A charges $60 to join plus $20 a month. Gym B has no joining fee and charges $30 a month. After how many months will they have cost the same?

    1. a) 10 months
    2. b) 6 months
    3. c) 2 months
    4. d) 3 months

  2. A rectangle's length is 3 cm more than twice its width, and its perimeter is 36 cm. What is its width?

    1. a) 7 cm
    2. b) 11 cm
    3. c) 5 cm
    4. d) 13 cm

  3. Solve 5 − 2x ≤ 11.

    1. a) x ≥ −3
    2. b) x ≤ −8
    3. c) x ≥ 3
    4. d) x ≤ −3

  4. Solve −2(x − 3) = 14.

    1. a) x = −8.5
    2. b) x = −4
    3. c) x = 10
    4. d) x = −10

  5. A club has $250. It spends $40 on supplies and wants to buy T-shirts at $12 each with the rest. What is the greatest number of T-shirts it can buy?

    1. a) 18
    2. b) 24
    3. c) 17
    4. d) 20

  6. Maddy has $45 saved and adds $12 a week. Which equation finds the number of weeks, w, until she has $153?

    1. a) 12 + 45w = 153
    2. b) 45 + 12w = 153
    3. c) 12w = 153
    4. d) 57w = 153

  7. Solve 3x + 7 = −8.

    1. a) x = −5
    2. b) x = 5
    3. c) x = −45
    4. d) x = −1/3

  8. Solve 12/x = −3.

    1. a) x = 4
    2. b) x = −4
    3. c) x = −1/4
    4. d) x = −36

  9. Student tickets to a school play cost $8 and adult tickets cost $12. In all, 150 tickets were sold for $1400. How many student tickets were sold?

    1. a) 100
    2. b) 70
    3. c) 175
    4. d) 50

  10. A number line shows an open circle at 2 with an arrow pointing left from it. Which inequality does it show?

    1. a) x ≤ 2
    2. b) x ≥ 2
    3. c) x > 2
    4. d) x < 2

Answer key · Linear equations and inequalities

Math 9 · maddyhelps.com

  1. b) 6 months — Set the costs equal: 60 + 20m = 30m, so 60 = 10m and m = 6. Check: 60 + 20(6) = 180 and 30(6) = 180 ✓. 60 ÷ 20 = 3 uses only Gym A's numbers, but the answer depends on the $10 a month difference between the gyms.
  2. c) 5 cm — Let the width be w, so the length is 2w + 3 and the perimeter is 2w + 2(2w + 3) = 6w + 6 = 36. Then 6w = 30 and w = 5 cm. Setting w + (2w + 3) = 36 uses only half the perimeter and gives 11, and 13 cm is the length, not the width.
  3. a) x ≥ −3 — Subtract 5: −2x ≤ 6. Divide by −2 and reverse the sign: x ≥ −3. Test x = 0: 5 − 0 = 5 ≤ 11 ✓, and 0 is in x ≥ −3; not reversing gives x ≤ −3, which leaves out 0 even though 0 works.
  4. b) x = −4 — Distribute: −2x + 6 = 14, so −2x = 8 and x = −4. Check: −2(−4 − 3) = −2(−7) = 14 ✓. The −2 times −3 is +6; writing −6 gives x = −10, and multiplying only the x gives −2x − 3 = 14 and x = −8.5.
  5. c) 17 — 40 + 12t ≤ 250 gives 12t ≤ 210, so t ≤ 17.5. The club cannot buy half a T-shirt, and 18 would cost 40 + 216 = $256, over budget, so the answer is 17. Rounding 17.5 up is the trap: with an inequality, the rounding has to stay inside the limit.
  6. b) 45 + 12w = 153 — The $12 is added every week, so it multiplies w, and the $45 is there once, at the start. 57w = 153 counts the $45 again every week. Solving the right equation gives 12w = 108, so w = 9 weeks.
  7. a) x = −5 — Subtract 7 from both sides: 3x = −15. Then divide by 3: x = −5, and check: 3(−5) + 7 = −8 ✓. Adding 7 instead of subtracting it gives 3x = −1 and x = −1/3.
  8. b) x = −4 — Multiply both sides by x: 12 = −3x, so x = 12 ÷ (−3) = −4. Check: 12 ÷ (−4) = −3 ✓. Multiplying 12 by −3 gives −36, which treats x as if it were on top of the fraction.
  9. a) 100 — Let s be the student tickets, so 150 − s are adult tickets: 8s + 12(150 − s) = 1400, which gives 1800 − 4s = 1400 and s = 100. 50 is the number of adult tickets — answer the question that was asked. 1400 ÷ 8 = 175 assumes every ticket was a student ticket, which is more than the 150 sold.
  10. d) x < 2 — An open circle means 2 itself is not included, so the sign is < or >, not ≤ or ≥. The arrow points left, towards smaller numbers, so x < 2.